# Properties

 Label 159120.du Number of curves $4$ Conductor $159120$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("du1")

sage: E.isogeny_class()

## Elliptic curves in class 159120.du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.du1 159120dg4 $$[0, 0, 0, -562467, -162364174]$$ $$26362547147244676/244298925$$ $$182368170316800$$ $$$$ $$1179648$$ $$1.9001$$
159120.du2 159120dg2 $$[0, 0, 0, -35967, -2413474]$$ $$27572037674704/2472575625$$ $$461441953440000$$ $$[2, 2]$$ $$589824$$ $$1.5535$$
159120.du3 159120dg1 $$[0, 0, 0, -7842, 224651]$$ $$4572531595264/776953125$$ $$9062381250000$$ $$$$ $$294912$$ $$1.2069$$ $$\Gamma_0(N)$$-optimal
159120.du4 159120dg3 $$[0, 0, 0, 40533, -11302774]$$ $$9865576607324/79640206425$$ $$-59451095535436800$$ $$$$ $$1179648$$ $$1.9001$$

## Rank

sage: E.rank()

The elliptic curves in class 159120.du have rank $$0$$.

## Complex multiplication

The elliptic curves in class 159120.du do not have complex multiplication.

## Modular form 159120.2.a.du

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} + q^{13} - q^{17} + 8q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 